Spikey... This is really bad news mate. I know it seems a bit trivial and its under the car so you're not going to see it but the point is, it's there, you know it's there and it has nothing to do with your neglect or any DiY mess up.
Ask yourself how else could the damage have been caused? Simple answer is it is obvious its been caused by a jack or part of the lift feet. The dealership is responsible and it would be obvious to any service manager worth their salt that the damaged part should be replaced without question.
If the car has never had a puncture in its life, you could argue further that the vehicle has never had to be jacked up at all before. This also begs the question that if this silly, simple slip was made, what else could they have done in an unseen area of your car. I would tactfully put that to them as well.
If they don't resolve this situation for you, every time you wash the car you will think about it and IMO, that is tainting your ownership of the car. Only in a small way, but you'll feel it. Hope you get it sorted.